We present a theoretical analysis of a possible new avalanching photodetector (APD) based on II-VI compound semiconductors. Each unit cell is comprised of a HgTe layer, or a similar semimetal, sandwiched between two layers of CdTe and HgCdTe or similar semiconducting materials. The barrier layers are graded so that the leading barrier height is as large as possible, whereas the trailing barrier height is just high enough to eliminate the thermionic emission dark current out of the well. The use of a semimetal within the well has a distinct advantage over a semiconductor, which is that the ionization process is essentially an interband mechanism since the confined carriers within the well lie within the overlaping conduction and valence bands. As a result, the concentration of target carriers is virtually inexhaustible as in a conventional interband device. In essence, this scheme combines the advantages of a confined state, i.e., unipolar ionizing and low-voltage operation, with some of those of interband avalanche photodetectors, i.e., a large target carrier concentration. It is found that, in principle, the gain of a HgTe-based device can be significant, whereas the dark current is negligible and the excess noise factor is less than two.